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Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n ver-tices of degree i. Essentially, we show that if P i(i?2) i > 0 then such graphs almost surely have a giant component, while if P i(i?2) i < 0 then almost surely all components in such graphs are small. We can apply these results(More)
Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider a random graph having approximately i n ver-tices of degree i. In 12] the authors essentially show that if P i(i ? 2) i > 0 then the graph a.s. has a giant component, while if P i(i ? 2) i < 0 then a.s. all components in the graph are small. In this paper we analyze the(More)
Recently there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Rather intriguingly, experimental results with various models for generating random CSP instances suggest a \threshold-like" behavior and some theoretical work has been done in analyzing these models when(More)
We introduce a class of models for random Constraint Satisfaction Problems. This class includes and generalizes many previously studied models. We characterize those models from our class which are asymptot-ically interesting in the sense that the limiting probability of satissability changes signiicantly as the number of constraints increases. We also(More)